How to Factor by GCF?
In this step-by-step guide, you will learn more about factoring polynomials by the greatest common factor.
Related Topics
Step-by-step guide to factoring by \(GCF\)
The process of factoring polynomials includes expressing the polynomial as a product of its factors. Factoring polynomials help to find the zeros of the polynomial expression or to find the values of the variables of the given expression.
There are several methods for factoring polynomials based on expressions. One of them is factoring based on the greatest common factor or \(GCF\). The \(GCF\) of a polynomial is the greatest monomial that divides the polynomial terms. Note that the \(GCF\) should be a factor of all terms in the polynomial.
The process of obtaining the greatest common factor for two or more terms involves two simple steps. First, divide each expression into its prime factors and then take as many common factors as possible from the given expressions.
Let us understand this using a simple expression of two terms \(15x^4 + 3x^3\). Here we split the terms into their prime factors \(15x^4 + 3x^3 = 5\times 3\times x\times x\times x\times x + 3\times x\times x\times x\). From these two terms, we can take the maximum common terms to get the greatest common factors. Here we have the maximum common factor as \(3x^3\), and hence \(15x^4 + 3x^3= 3x^3(5x + 1)\).
Factoring by \(GCF\) – Example 1:
Factor the polynomial. \(12y^3-27y^2\)
Solution: First, find the \(GCF\) of all of the terms:
\(12y^3=2×2×3×y×y×y\) , \(27y^2=3×3×3×y×y\). The common factors are \(3×y×y\). And, the \(GCF\) is \(3y^2\).
So \(12y^3-27y^2 = 3y^2(4y-9)\).
Related to This Article
More math articles
- ISEE Middle-Level Math Worksheets: FREE & Printable
- Top 10 CHSPE Math Practice Questions
- Intelligent Math Puzzle – Challenge 82
- GED Math Question Types
- 10 Most Common 4th Grade IAR Math Questions
- The Ultimate 7th Grade OSTP Math Course (+FREE Worksheets)
- FTCE General Knowledge Test Review
- How to Graph Polynomial Functions
- HSPT Math-Test Day Tips
- 5th Grade ACT Aspire Math FREE Sample Practice Questions
What people say about "How to Factor by GCF? - Effortless Math: We Help Students Learn to LOVE Mathematics"?
No one replied yet.